Question:
Find X,if \(Y=\begin{bmatrix}3&2\\1&4\end{bmatrix}\)and \(2X+Y=\begin{bmatrix}1&0\\-3&2\end{bmatrix}\)
Find X,if \(Y=\begin{bmatrix}3&2\\1&4\end{bmatrix}\)and \(2X+Y=\begin{bmatrix}1&0\\-3&2\end{bmatrix}\)
Updated On: Sep 4, 2023
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Solution and Explanation
The correct answer is \(\begin{bmatrix}-1&-1\\-2&-1\end{bmatrix}\)
\(2X+Y=\begin{bmatrix}1&0\\-3&2\end{bmatrix}\)
\(\implies 2X+\begin{bmatrix}3&2\\1&4\end{bmatrix}=\begin{bmatrix}1&0\\-3&2\end{bmatrix}\)
\(\implies 2X=\begin{bmatrix}1&0\\-3&2\end{bmatrix}-\begin{bmatrix}3&2\\1&4\end{bmatrix}=\begin{bmatrix}1-3&0-2\\-3-1&2-4\end{bmatrix}\)
\(\implies 2X=\begin{bmatrix}-2&-2\\-4&-2\end{bmatrix}\)
\(\therefore X=\frac{1}{2}\begin{bmatrix}-2&-2\\-4&-2\end{bmatrix}=\begin{bmatrix}-1&-1\\-2&-1\end{bmatrix}\)
\(2X+Y=\begin{bmatrix}1&0\\-3&2\end{bmatrix}\)
\(\implies 2X+\begin{bmatrix}3&2\\1&4\end{bmatrix}=\begin{bmatrix}1&0\\-3&2\end{bmatrix}\)
\(\implies 2X=\begin{bmatrix}1&0\\-3&2\end{bmatrix}-\begin{bmatrix}3&2\\1&4\end{bmatrix}=\begin{bmatrix}1-3&0-2\\-3-1&2-4\end{bmatrix}\)
\(\implies 2X=\begin{bmatrix}-2&-2\\-4&-2\end{bmatrix}\)
\(\therefore X=\frac{1}{2}\begin{bmatrix}-2&-2\\-4&-2\end{bmatrix}=\begin{bmatrix}-1&-1\\-2&-1\end{bmatrix}\)
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